3. THE KINEMATICS OF THE BLR AND TORUS

The kinematics of the BLR have been a long-standing problem. It has been
known from the earliest days of AGN studies that the lines are very
broad (for a review of the earliest literature see
Seyfert 1943),
but Doppler shifts only tell us the motion of gas along the line of
sight. To know whether the gas is inflowing, outflowing, moving in
random virialized orbits, or in more planar Keplerian orbits in a disc
we need to know the line-of-sight velocity as a function of position
relative to the black hole.

The discovery of narrow intrinsic absorption in NGC 4151
(Mayall 1934,
Anderson
& Kraft 1969)
and of broad absorption lines (BALs) in PHL 5200
(Lynds 1967)
proved that some
gas was outflowing from AGNs. However, BALs commonly extend to
velocities several times higher than those observed for the BLR in the
same objects (see, for example,
Turnshek et
al. 1988),
so it is not clear that there is necessarily any connection between BALs and
BLRs. The case for an outflowing BLR was strengthened though when
Blumenthal
& Mathews (1975)
and
Baldwin (1975)
showed that a radiatively-accelerated outflow could reproduce the
observed line profiles well in some objects. However,
Capriotti,
Foltz, & Byard (1980)
showed that other models could provide comparably good
fits to broad-line profiles, and so demonstrated that fits to individual
line profiles alone could not uniquely determine the kinematics.

More progress was made by comparing lines of differing ionizations.
Gaskell (1982)
discovered that high-ionization broad lines were blueshifted with respect to
low-ionization lines, and pointed out that this requires there to be
radial motions plus some source of opacity. This blueshifting
has now been widely confirmed.
Gaskell (1982)
suggested that the blueshifting could be the result of a
"disk-wind" model where the high-ionization lines arise in a wind
outflowing above the accretion disc.
Wilkes
& Carswell (1982)
pointed out a problem with any purely radial motion: the
profiles of C IV and Lyman
were observed to be
very similar, yet, for optically-thick clouds, Lyman
is emitted very
anisotropically. To satisfy this constraint the clouds either had to be
optically thin, or not moving purely radially.

Figure 8. Velocity-resolved reverberation
mapping. Because of light-travel-time effects, the gas on the near side
of the AGN is seen to respond to continuum changes first. For the the
hypothetical outflowing BLR illustrated here, the blue wing of
a line would vary first.

Figure 9. The cross-correlation function
for the blue and red wings of the Mg II line in NGC 4151 as a
function of time delay. The predicted peak in the correlation function
for pure outflow (blue wing varies first) is shown by the arrow. It can
be seen instead that the strongest correlation is for near zero delay
(what is expected for virialized or Keplerian motion), but with the red
wind leading by a small but significant amount thus implying some net
inflow. Figure from
Gaskell
(1988).

While the velocity-resolved reverberation mapping results were good news
for the new black-hole-mass-determination industry, they created a
problem for the generally accepted "disk-wind" explanation of the
blueshiftings of high-ionization lines. Disk-wind models are very
theoretically appealing, and strong blueshiftings have been taken as
signs of strong winds (e.g.,
Leighly
& Moore 2004).
However, at the same time, people working on black hole
mass determinations were firmly believing that they were using
virialized lines! This has almost caused AGN observers to suffer from
multiple-personality disorder!
3,4

Figure 10. Cartoon illustrating why
scattered photons are blueshifted when scattered off a reflector which
is approaching the source of photons. The person on the right sees her
reflection (far left) in the mirror. If the mirror is approaching her,
then the image is approaching her twice as quickly.

We have used the STOKES Monte Carlo radiative transfer code
(Goosmann
& Gaskell 2007)
5 to model the
effects on line profiles of scattering off an inflowing external
medium. The two geometries considered are shown in
Fig. 11. One is an
infalling spherical distribution of scatterers and the other an
infalling cylindrical distribution. In Fig. 12
we show a comparison of
observed profiles of two low- and high- ionization lines in
PKS 0304-392 with various models with. We adopted an
infall velocity of ~ 1000 km s-1 based on
velocity-dependent reverberation mapping, spectropolarimetry, and the
observed mean blueshift (see
Gaskell
& Goosmann 2008
for details). It can be seen that both spherically and
cylindrically symmetric models readily reproduce the blueshifting.

Figure 11. Cross sections in a plane
through the axis of symmetry of the two scattering region geometries
modeled in Fig. 12.

Figure 12. Modelling the blueshifting of
high-ionization lines. The profiles of O I
1305 (narrow
symmetric profile shown in red) and C IV
1549 (thick blue
line) for the quasar PKS 0304-392. The thin black line is the
blueshifted profile produced by an infalling spherical distribution of
external scatters with an electron-scattering optical depth
es = 0.5, and
the dashed green line is the profile produced by the same distribution
with es = 1. The
brown dots are the profile produced
by a es = 20
infalling external cylindrical distribution. The geometries are shown in
Fig. 11. Figure from
Gaskell
& Goosmann (2008);
PKS 0304-392 observations taken from
Wilkes
(1984).

An additional advantage of having significant scattering in the BLR is
that it solves the "smoothness problem" for BLR line profiles
(Capriotti,
Foltz, & Byard 1981).
The intrinsic line broadening in an individual BLR
cloudlet is only of the order of the sound speed (~ 15 km
s-1), yet the velocity broadening of the BLR as a whole
is hundreds of times greater. This requires the number of clouds to be
very high
(Capriotti,
Foltz, & Byard 1981,
Atwood et
al. 1982).
The limit on the number of discrete clouds has now
been pushed up to 108
(Arav et al. 1998,
Dietrich et
al. 1999).
This constraint is relaxed if there is broadening by scattering.

For a typical AGN, several independent lines of evidence (the
blueshifting, velocity-resolved reverberation mapping, and
spectropolarimetry) all point to the inflow velocity being of the order
of ~ 1000 km s-1. As has been mentioned,
velocity-resolved reverberation mapping (see, for example,
Fig. 9)
implies that the dominant motion is not radial, but
Keplerian or random. The observed widths of broad lines are indeed
several times higher than the inflow velocity, and, of course, the
predominant motion for a flattened distribution must be Keplerian.

As is clear from Fig. 6 and
7, when we observe the BLR (i.e.,
in type-1 objects) we are always seeing it close to face-on. The
Keplerian component of velocity must be reduced by sini, where
i is the angle between the axis of rotational symmetry and the
line of sight. The statistics of line profiles in the SDSS
(La Mura et
al. 2009)
suggest that for the vast majority of objects i is < 20deg).

As was realized by
Osterbrock
(1978),
the statistics of line widths imply that, in addition to
Keplerian motion, there has to be a substantial additional component of
velocity perpendicular to the orbital plane. Osterbrock
appropriately called this "turbulence". The vertical component is also
necessary for the reconciling the structure of the BLR with its
kinematics. As
Mannucci,
Salvati, & Stranga (1992)
showed, for NGC 5548 the combined
constraints of reverberation mapping and time-averaged line profile and
favor the sort of "bird's nest" BLR distribution shown in
Figs. 6 and
7.

In summary, I believe that all the evidence points to the BLR having a
nest-like appearance and having velocity components:

(1)

where the Keplerian velocity, vKepler, of an
emission line is a couple of times larger that the turbulent velocity,
vturb, which is in turn somewhat bigger than
the inflow velocity, inflow. The ratios of BLR height to radius
and of vKepler to
vturb are similar to those deduced by
Osterbrock
(1978).
The only change to the Osterbrock model is recognizing that there is
also a significant inflow.

2 The BLR was first used to estimate
masses of AGN black holes by
Dibai (1977)
who estimated BLR sizes using photoionization considerations. At that
stage, of course, there was no clear evidence that the BLR was
virialized. See
Bochkarev
& Gaskell (2009).
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3 or at the very least to fear that, like
the White Queen in Alice in Wonderland, they might have to
believe in six impossible things before night lunch!
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4 The narrow-line region is creating a
similar problem. People who study extended narrow-line emission
associate it with jets and outflows, while other people are using
narrow-line velocity widths as a proxy for the stellar velocity
dispersion (see
Gaskell 2009a).
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